Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements

Abstract

Floquet codes are an intriguing generalisation of stabiliser and subsystem codes, which can provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware. A recent question of interest has been how to run Floquet codes on devices which have defective -- and therefore unusable -- qubits. This is an under-studied issue of crucial importance for running such codes on realistic hardware. To address this challenge, we introduce a new method of accommodating defective qubits on a wide range of two-dimensional Floquet codes, which requires no additional connectivity in the underlying quantum hardware, no modifications to the original Floquet code's measurement schedule, can accommodate boundaries, and is optimal in terms of the number of qubits and stabilisers removed. We numerically demonstrate that, using this method, the planar honeycomb code is fault tolerant up to a fabrication defect probability of $\approx 12\%$. We find the fault-tolerant performance of this code under defect noise is competitive with that of the surface code, despite its sparser connectivity. We finally propose multiple ways this approach can be adapted to the underlying hardware, through utilising any additional connectivity available, and treating defective auxiliary qubits separately to defective data qubits. Our work therefore serves as a guide for the implementation of Floquet codes in realistic quantum hardware.

37 pages, 22 figures, minor updates based on referee comments

References in corpus (34)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Suppressing quantum errors by scaling a surface code logical qubit
• Topological Quantum Distillation
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Stim: a fast stabilizer circuit simulator
• Impact of ionizing radiation on superconducting qubit coherence
• Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits
• Dynamically Generated Logical Qubits
• Fault tolerant quantum computation with very high threshold for loss errors
• Coping with qubit leakage in topological codes
• Error Correction and Degeneracy in Surface Codes Suffering Loss
• Overcoming leakage in scalable quantum error correction
• A Fault-Tolerant Honeycomb Memory
• Understanding the effects of leakage in superconducting quantum error detection circuits
• High threshold codes for neutral atom qubits with biased erasure errors
• Floquet codes without parent subsystem codes
• Anyon condensation and the color code
• Boundaries for the Honeycomb Code
• Performance of planar Floquet codes with Majorana-based qubits
• High-threshold quantum computing by fusing one-dimensional cluster states
• Benchmarking the Planar Honeycomb Code
• Fault-tolerance thresholds for the surface code with fabrication errors
• Fault-tolerant quantum computation with non-deterministic entangling gates
• Surface Code Error Correction on a Defective Lattice
• Handling Leakage with Subsystem Codes
• Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
• Practical Topological Cluster State Quantum Computing Requires Loss Below 1%
• Engineering 3D Floquet codes by rewinding
• Quantum computation from dynamic automorphism codes
• Floquetifying the Colour Code
• Adaptive surface code for quantum error correction in the presence of temporary or permanent defects
• Q3DE: A fault-tolerant quantum computer architecture for multi-bit burst errors by cosmic rays
• Improved Pairwise Measurement-Based Surface Code

Cited by in corpus (5)

• Fundamental thresholds for computational and erasure errors via the coherent information
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Magic State Injection on IBM Quantum Processors Above the Distillation Threshold
• Competing automorphisms and disordered Floquet codes
• Phases of Floquet code under local decoherence